Transformation of Functions

Front

What is a horizontal shift in a function?

Back

A horizontal shift occurs when the function is transformed by adding or subtracting a value from the input variable (x). For example, f(x + c) shifts the graph left by c units if c is positive and right by c units if c is negative.

Front

What does the transformation f(x) + k represent?

Back

The transformation f(x) + k represents a vertical shift of the graph. If k is positive, the graph shifts up by k units; if k is negative, it shifts down by k units.

Front

Describe the transformation of f(x) = f(x - 2).

Back

The transformation f(x) = f(x - 2) represents a horizontal shift to the right by 2 units.

Front

What does a vertical stretch of a function mean?

Back

A vertical stretch occurs when the output of the function is multiplied by a factor greater than 1. For example, f(x) becomes af(x) where a > 1 stretches the graph vertically.

Front

What is the effect of a negative sign in front of a function, such as -f(x)?

Back

The negative sign reflects the graph of the function across the x-axis.

Front

How does the transformation f(x) = f(-x) affect the graph?

Back

The transformation f(x) = f(-x) reflects the graph of the function across the y-axis.

Front

What is the transformation of f(x) = 2f(x)?

Back

The transformation f(x) = 2f(x) represents a vertical stretch by a factor of 2.

Front

Explain the transformation f(x) = f(x) - 4.

Back

The transformation f(x) = f(x) - 4 shifts the graph down by 4 units.

Front

What does the transformation f(x) = f(x + 5) indicate?

Back

The transformation f(x) = f(x + 5) indicates a horizontal shift to the left by 5 units.

Front

What is the transformation of f(x) = (x + 1)^2 + 3?

Back

The transformation f(x) = (x + 1)^2 + 3 shifts the graph left by 1 unit and up by 3 units.